Báo cáo toán học: "Asymptotics of coefficients of multivariate generating functions: improvements for smooth points" potx

... Recurrences for sums of powers of binomial coefficients, J. Comb. Theory Ser. A 52 (1989), 77–83. [McI] Richard J. McIntosh, Recurrences for alternating sums of powers of binomial coefficients, J. ... form if s is an integer ≥ 3. The idea of his proof was to compare the actual asymptotic behavior of the given sum, for fixed s and n →∞, with the asymptotic behavior of a hypoth...

Ngày tải lên: 07/08/2014, 06:22

... properties of the set of the hook numbers for some special families of (fixed) skew-Young diagrams (Theorem1.2). The problem appeared in the study of the hook formula for various kinds of Young ... problem appeared in the study of the hook formula for various kinds of Young diagrams. The proofs are based on properties of shifted Schur functions, due to Okounkov and Olshan...

Ngày tải lên: 07/08/2014, 06:20

... Euler characteristic of the surface, B depends on the type of map, and A depends on both the type of map and the surface. See [22] for a proof of (7) for the unrooted case and for further references. Zvonkin ... proof of (4), we estimate a n .WehaveA(x)=A(x, 1) = L(x, 1)U(x, 1). From LC, the coefficients of L(x, 1) are asymptotic to e C(R) c n . The radius of convergence...

Ngày tải lên: 07/08/2014, 06:20

... n)=  w 1 ···w n   1 ≤ w i ≤ k for all 1 ≤ i ≤ n  denote the set of words of length n on the alphabet {1, ···,k}.Awordw = w 1 ···w n ∈ W (k, n) is said to have a descent of length  if there exist ... in columns. Let s k (λ) denote the number of such k-tableaux. It is well known that s k (λ)is the degree of a corresponding irreducible character of GL(k, C) (or of SL(k, C))....

Ngày tải lên: 07/08/2014, 06:22

... last claim in the theorem. 9 Proofs of Theorems 1 and 2 All mentions of Run(···) in Theorem 1 are divided by factorials and so can be thought of as functions of the form f(∗, ∗,γ) according to Lemma ... (For the “end” values, B 0 = C 0 and B k = C k .) This complication is taken care of by writing down the same formula for all the L i empty and dividing one formula by the other,...

Ngày tải lên: 07/08/2014, 08:20

... need the same arguments from the proof of Lemma 2 in our proof of Theorem 1, we will include the full proof of Lemma 2 there. As examples of these lemmas, for the symmetric group, which has m ... number of standard tableaux of shape µ of size k is the multiplicity of the representation with highest weight µ in the kth tensor power of the defining representation of GL n ,...

Ngày tải lên: 07/08/2014, 08:22

... Babai, The probability of generating the symmetric group, J. Combin. Theory (Ser. A) 52 (1989) 148–153. [2] E.A. Bender, An asymptotic expansion for some coefficients of some formal power series, ... t n has an asymptotic expansion of the form 1 +  ∞ k=1 c k n −k where c k =  k−1 i=1 S(k −1,i)d i+1 since S(m, 0) = 0 for m = 0. To compute the numerical values of the coefficients...

Ngày tải lên: 07/08/2014, 13:21

... the average height of p– watermelons with a wall in terms of certain determinants. Moreover, we make these formulas more explicit (in terms of sums of binomial coefficients) for the simple cases ... classical work of de Bruijn, Knuth and Rice (giving the asymp- totics of the average height of Dyck paths of length n) to the case of p–watermelons with a wall (i.e., to a certa...

Ngày tải lên: 07/08/2014, 15:23

... very idea of IF. The shape of p, as a function of d, is shown in Figure 5, for different values of c and ρ s . It can be observed that the PAF of SIF is monotonically increasing and concave for all ... increasing and concave for all values of c. Moreover, it becomes selective far small values of c (e.g., 1), while it tends to flatten for high values of c and for low va...

Ngày tải lên: 20/06/2014, 20:20

... pres- sure of 5.0 × 10 -5 Torr. A 50-mm diameter ZnS target (99.99%) was used for sputtering. In order to clean the sur- face of the target, pre-sputtering for 10 min was per- formed with an RF power of ... the large amount of cadmium-containing waste during the deposi- tion process. Therefore, the development of a Cd-free buffer layer is one of the major objectives in the fie...

Ngày tải lên: 20/06/2014, 21:20